Question

The quality control team of a company checked 800 digital cameras for defects. The team found that 20 cameras had lens defects, 25 cameras had charging defects, and 6 cameras had both defects. What is the probability that a camera has a lens defect given that it has a charging defect?

Answer 1

0.025

Explanation:

-This is a conditional probability problem.

-Let L denote lens defect and C charging defect.

#We first calculate the probability of a camera having a lens defect;

`P(lens)=(Lens)/(Total)\\\\=(20)/(800)\\\\=0.025`

#Calculate the probability of a camera having a charging defect:

`P(Charging)=(Charging)/(Total)\\\\=(25)/(800)\\\\=0.03125`

The the probability that a camera has a lens defect given that it has a charging defect is calculated as:

`P(L|C)=(P(C)P(L))/(P(C))\\\\=(0.025* 0.03125)/(0.03125)\\\\=0.025`

Hence, the probability that a camera has a lens defect given that it has a charging defect is 0.025